In the previous paper, the authors proposed a new type of magnetic damper using a lever-type displacement magnifying mechanism and rare-earth magnets. In this paper, a viscoelastic-friction damper and a viscoelastic damper using the lever-type displacement magnifying mechanism and viscoelastic material are proposed in order to obtain a passive damper which gives damping and stiffness within a relative displacement in the region of about 0.1∼20 mm. Denoting the magnifying ratio by λ, the damping force and the spring force of the viscoelastic material are increased λ2 times and the friction force is increased λ times by the magnifying mechanism. The trial dampers were made and the resisting force characteristics were measured. To describe the mathematical properties of the viscoelastic material, a four-element viscoelastic model was used, and the parameters of the model were identified using the experimental results. The frequency responses and the seismic responses of a three-dimensional piping system supported by each damper were measured using an electrohydraulic type shaking table. The experimental results are compared with the calculated results obtained by the finite element method (ANSYS), and the effects of vibration suppression of the dampers are discussed.